Let's break this down step by step. You need to form four-digit sequences using the digits 1, 2, 3, 4, 5, but the last two digits must be combined into one number (e.g., "45" or "23").

Approach:

1. You select three digits from {1, 2, 3, 4, 5} for the first three positions.
2. The remaining two digits will form a two-digit number at the end.

Listing all possible combinations:

• First, let's list all possible choices of three digits out of the five.
• Then, for each choice of three digits, we'll attach the possible two-digit combinations from the remaining two digits.

Here are the combinations:

1. 1, 2, 3, 45
2. 1, 2, 4, 35
3. 1, 2, 5, 34
4. 1, 3, 2, 45
5. 1, 3, 4, 25
6. 1, 3, 5, 24
7. 1, 4, 2, 35
8. 1, 4, 3, 25
9. 1, 4, 5, 23
10. 1, 5, 2, 34
11. 1, 5, 3, 24
12. 1, 5, 4, 23
13. 2, 1, 3, 45
14. 2, 1, 4, 35
15. 2, 1, 5, 34
16. 2, 3, 1, 45
17. 2, 3, 4, 15
18. 2, 3, 5, 14
19. 2, 4, 1, 35
20. 2, 4, 3, 15
21. 2, 4, 5, 13
22. 2, 5, 1, 34
23. 2, 5, 3, 14
24. 2, 5, 4, 13
25. 3, 1, 2, 45
26. 3, 1, 4, 25
27. 3, 1, 5, 24
28. 3, 2, 1, 45
29. 3, 2, 4, 15
30. 3, 2, 5, 14
31. 3, 4, 1, 25
32. 3, 4, 2, 15
33. 3, 4, 5, 12
34. 3, 5, 1, 24
35. 3, 5, 2, 14
36. 3, 5, 4, 12
37. 4, 1, 2, 35
38. 4, 1, 3, 25
39. 4, 1, 5, 23
40. 4, 2, 1, 35
41. 4, 2, 3, 15
42. 4, 2, 5, 13
43. 4, 3, 1, 25
44. 4, 3, 2, 15
45. 4, 3, 5, 12
46. 4, 5, 1, 23
47. 4, 5, 2, 13
48. 4, 5, 3, 12
49. 5, 1, 2, 34
50. 5, 1, 3, 24
51. 5, 1, 4, 23
52. 5, 2, 1, 34
53. 5, 2, 3, 14
54. 5, 2, 4, 13
55. 5, 3, 1, 24
56. 5, 3, 2, 14
57. 5, 3, 4, 12
58. 5, 4, 1, 23
59. 5, 4, 2, 13
60. 5, 4, 3, 12

These are all the possible combinations using the digits 1, 2, 3, 4, and 5 to form a 4-digit sequence where the last two digits are combined.

Would you like more details or have any questions?

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5 Related Questions:

1. How can we calculate how many total combinations there are?
2. What if we allow repetition of digits in this problem?
3. How would the result change if no digits could repeat in the sequence?
4. Can you generalize this approach to a larger set of numbers (e.g., digits 1 to 6)?
5. How can we automate this process using programming?

Tip:

For problems like this involving combinations and permutations, using systematic approaches like "choose and arrange" can help ensure all cases are covered.